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Complicated nonlinear responses of a simply supported FGM rectangular plate under combined parametric and external excitations

Content Provider	Springer Nature Link
Author	Zhang, Wei Hao, Yuxin Guo, Xingying Chen, Lihua
Copyright Year	2011
Abstract	In this paper, we use the asymptotic perturbation method based on the Fourier expansion and the temporal rescaling to investigate the nonlinear oscillations and chaotic dynamics of a simply supported rectangular plate made of functionally graded materials (FGMs) subjected to a through-thickness temperature field together with parametric and external excitations. Material properties are assumed to be temperature-dependent. Based on the Reddy’s third-order plate theory, the governing equations of motion for the plate are derived using the Hamilton’s principle. The Galerkin procedure is employed to obtain a two-degree-of-freedom nonlinear system including the quadratic and cubic nonlinear terms. The resonant case considered here is 1:2 internal resonance, principal parametric resonance-1/2 subharmonic resonance. Based on the averaged equation in polar coordinate form, the stability of steady state solutions is analyzed. The phase portrait, waveform and Poincaré map are used to analyze the periodic and chaotic motions of the FGM rectangular plate. It is found that the FGM rectangular plate exhibits the chaotic motions under certain circumstances. It is seen that the nonlinear dynamic responses of the FGM rectangular plate are more sensitive to transverse excitation. The excitation force can be used as a controlling factor which can change the response of the FGM rectangular plate from periodic motion to the chaotic motion.
Starting Page	985
Ending Page	1014
Page Count	30
File Format	PDF
ISSN	00256455
Journal	Meccanica
Volume Number	47
Issue Number	4
e-ISSN	15729648
Language	English
Publisher	Springer Netherlands
Publisher Date	2011-11-04
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Functionally graded materials Rectangular plates Asymptotic perturbation method Chaotic motion Higher-order plate theory Poincaré map Mechanical Engineering Civil Engineering Mechanics Automotive Engineering
Content Type	Text
Resource Type	Article
Subject	Mechanics of Materials Condensed Matter Physics Mechanical Engineering

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Nonlinear dynamics of a simply supported FGM rectangular plate under combined parametrical and external excitations

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